User:Kdsaurav/Resonant Cavity Enhanced Photodetectors

Resonant Cavity Enhanced Photo Detectors (or, RCE photo detectors) has improved performance over its predecessors by placing the active device structure inside a Fabry-Perot resonant cavity. Though the active device structure of the RCE detectors remains close to other conventional photodetectors, the effect of the resonant cavity, which allows wavelength selectivity and an enhancement of the optical field due to resonance, allows the photo detectors to be made thinner and therefore faster, while simultaneously increasing the quantum efficiency at the resonant wavelengths.

Advantages
The quantum efficiency of conventional detectors is dominated by the optical absorption of the semiconductor material. For semiconductors with low absorption coefficients, a thicker absorption regions is required to achieve higher quantum efficiency, but at the cost of the bandwidth of Photodetectors.

A RCE detector improves the bandwidth significantly. The constructive interference of a Fabry–Perot cavity enhances the optical field inside the photodetector at the resonance wavelengths to achieve a quantum efficiency of close to unity. Moreover the resonant cavity makes the RCE detectors wavelength selective. This makes RCE photodetectors attractive for low crosstalk wavelength demultiplexing. Improved quantum efficiency gives less power consumption. Higher bandwidth gives faster operation.

The RCE photodetectors have both wavelength selectivity and high speed response making them ideal for wavelength division multiplexing applications. Optical modulators situated in a resonant cavity require fewer quantum wells to absorb the same fraction of the incident light, and can therefore operate at lower voltages. In the case of emitters, the cavity modifies the spontaneous emission of light emitting diodes (LED) improving their spectral purity and directivity.

Thus optical communication systems can perform much faster, with more bandwidth and can become more reliable. Camera sensors could give more resolutions, better contrast ratios and less distortion. For these reasons, RCE devices can be expected to play a growing role in optoelectronics over the coming years.

Theory of RCE Photo detectors
The RCE photo detectors can provide:
 * 1.Higher Quantum efficiency,
 * 2.Higher detection speed,
 * 3.Wavelength selective detection,

than compare to a conventional photodiode.

Quantum Efficiency of RCE Photo detectors
The RCE photodetectors are expected to have higher quantum efficiency η than compare to conventional photodiodes. The formulation of η for RCE devices gives insight to the design criteria.

A generalized RCE photodetector schematic as given in Figure 1 can give the required theoretical model of photodetection. A thin absorption region of thickness d is sandwiched between two relatively less absorbing region, substrate, of thickness L1 and L2. The optical cavity is formed by a period of λ/4 distributed Bragg reflector (DBR), made of non-absorbing larger bandgap materials, at the both end of the substrate. The front mirror has a transmittance of t1 and generally has lower reflectivity than compare to the mirror at back (R1 < R2 ). Transmittance t1 allows light to enter into the cavity, and reflectivity R1 (=r12) and R2 (=r22) provides the optical confinement in the cavity.

The active region and the substrate region have absorption coefficient α and αex respectively. The field reflection coefficients of the front and the back mirrors are $$r_1 e^{-j\phi_1}$$ and $$r_2e^{-j\phi_2}$$ respectively, where ф1 and ф2 are the phase shifts due to the light penetration into the mirrors. The optical microcavity allows building up an optical field inside the resonator cavity. In compare to conventional detector, where light is absorbed in a single pass through the absorption region, for RCE detectors trapped light is absorbed each time it traverses through the absorption region.

The Quantum efficiency $$\eta$$ for a RCE detector is given by:


 * $$\eta=(1-R_1)(1-e^{-\alpha d} )[ \frac {( e^{-\alpha_{ex} L_1} +r_2^2 e^{-\alpha_{ex} L_2 - \alpha_c L} )}{1 - 2 r_1 r_2 e^{- \alpha_c L}\cos(2\beta L+ \phi_1 + \phi_2) + (r_1r_2)^2 e^{- \alpha_c L}}] $$

Here αc = (αexL1 + αexL2 + αd)/L. In practical detector design αex << α, so αex can be neglected and $$\eta$$ can be given as:


 * $$\eta=(1-R_1)(1-e^{-\alpha d} )[ \frac {( 1 +R_2 e^{-\alpha d} )}{1 - 2 \sqrt{R_1 R_2} e^{- \alpha_c d}\cos(2\beta L+ \phi_1 + \phi_2) + (R_1 R_2) e^{- \alpha_c d}}] $$

The term inside the [] represents the cavity enhancement effect. This is a periodic function of 2βL+ ф1 + ф2, which has minima at 2βL+ ф1 + ф2 = 2mп. And η enhanced periodically at resonant wavelength that meets this condition. The spacing of the resonant wavelength is given by the Free Spectral Range of the cavity.

The peak value of η at resonant wavelength is given as:


 * $$\eta=(1-R_1)(1-e^{-\alpha d} )[ \frac {( 1 +R_2 e^{-\alpha d} )}{(1 - \sqrt{R_1 R_2} e^{- \alpha_c d})^2}] $$

for a thin active layer as αd<<1, η becomes:


 * $$\eta=(1-R_1)\alpha d [ \frac {( 1 +R_2 e^{-\alpha d} )}{(1 - \sqrt{R_1 R_2} e^{- \alpha_c d})^2}] $$

This is a significant improve from the Quantum Efficiency of a conventional photodetector which is given by:


 * $$\eta=(1-R) \alpha L$$.

This shows that higher quantum efficiency can be achieved for smaller absorption region.

The critical design requirements are : a very high back mirror reflectivity and a moderate absorption layer thickness. At optical frequencies metal mirrors have low reflectivity (94%) when used on materials like GaAs. This makes metal mirrors inefficient for RCE detection. Whereas distributed Bragg reflector (DBR) can provide reflectivity near unity, are ideal choices for RCE structures.

For a R2=0.99 and α=104 cm-1 with a R1=0.2 a η of 0.99 or more can be achievable for d=0.7-0.95µm. Similarly for different values of R1 very high η is possible to achieve. However, R1 =0 limits the length of thickness region, d>5 µm can achieve 0.99 η but at the cost of bandwidth.

Detection speed of RCE Photodiodes
The detection speed depends upon the drift velocities of the electrons and holes. And between these two holes have slower drift velocity than the electrons. The transit time limited bandwidth of conventional p-i-n photodiode is given by:


 * $$f_{transit} =0.45\frac{v_h}{L}$$

However the quantum efficiency is a function of L as:


 * $$\eta=(1-R) \alpha L$$.

For a high speed detector for a small value of L, as α is very small, η becomes very small (η<<1). This shows for a optimum value of quantum efficiency the bandwidth has to sacrifice.

A p-i-n RCE photodetector can reduce the absorption region to a much smaller scale. In this case the carriers need to traverse a smaller distance as well, L1 (< L) and L2 (< L) for electrons and holes respectively.

The length of L1 and L2 can also be optimized to match the delay between the hole and electron drift. And the transition bandwidth becomes:


 * $$f_{transit} =0.45\frac{v_h + v_e}{L+d}$$

As in most of semiconductors $$v_e$$ is more than $$v_h$$ the bandwidth increases drastically.

It’s been reported that for a large device of L=0.5μm 64GHz of bandwidth can be achieved and a small device of L=0.25μm can give 120GHz bandwidth, where conventional photodetectors have bandwidth of 10-30GHz.

Wavelength selectivity of RCE Photo detectors
A RCE structure can make the detector wavelength selective to an extent due to the resonance properties of the cavity. The resonance condition of the cavity is given as 2βL+ ф1 + ф2 = 2mп. For any other value the efficiency η reduces from its maximum value, and vanishes when 2βL+ ф1 + ф2 = (2m+1)п. The wavelength spacing of the maxima of η are separated by the Free Spectral Range of the cavity, given as:


 * $$FSR=\frac {\lambda^2} {2 n_{eff} (L + L_{eff,1} + L_{eff,2})}$$

Where neff is the effective refractive index and Leff,i are the effective optical path lengths of the mirrors.

Finesse, the ratio of the FSR to the FWHM at the resonant wavelength, gives the wavelength selectivity of the cavity.


 * $$Finesse= \frac{\pi(R_1R_2)^{1/4} e^{-\frac{\alpha d}{2}}} {(1 - \sqrt{R_1 R_2} e^{- \alpha_c d})^2} $$

This shows that the wavelength selectivity increases with higher reflectivity and smaller values of L.

Material Requirements for RCE Devices
The estimated superior performance of the RCE devices critically depends on the realization of very low loss active region. This enforces the conditions that: the mirror and the cavity materials must be non-absorbing at the detection wavelength; and the mirror should have very high reflectivity so that it gives highest optical confinement inside the cavity.

The absorption in the cavity can be limited by making the bandgap of the active region smaller than the cavity and the mirror. But a large difference in the bandgap would be a blockage in extraction of photo generated carriers from a heterojunction. Usually a moderate offset is kept within the absorption spectrum.

Different material combinations satisfy all of the above criteria and are therefore useable to the RCE scheme. Some material combinations used for RCE detection are:


 * 1.GaAs(M,C) / AlGaAs(M) / InGaAs(A) near 830-920nm.
 * 2.InP(C) / In0.53Ga0.47As(M) / In0.52Al0.48As(M) / In0.53-0.7GaAs(A) near 1550nm.
 * 3.GaAs(M,C) / AlAs(M) / Ge(A) near 830-920nm.
 * 4.Si(M,C) / SiGe(M) / Ge(A) near 1550nm.
 * 5.GaP(M) / AlP(M) / Si(A,S) near visible region.

Future of RCE Photodiodes
There are many examples of RCE devices, like p-i-n photodiode, avalanche photodiode, schottky diode are made that verifies the theory successfully. Some of them are in use in practical purposes as well as there is a future prospect in use as modulators, optical logics in Wavelength Division Multiplexing (WDM) systems which could enhance the quantum efficiency, operating bandwidth, wavelength selectivity.

RCE detectors are preferable in potential price and performance in commercial WDM systems. RCE detectors have very good potential for implementations in WDM systems and improve the performance significantly. There are various implementations of RCE modulators are made and there is a huge scope for further improvement in performance of those. Other than the photodetectors the RCE structures have lots of other implementations and a very high potential for improved performance. A Light Emitting Diode (LED) can be made to have narrower spectrum and higher directivity to allow more coupling to optical fibre and better utilization of the fibre bandwidth. Optical amplifiers can be made to have more compact, thus lower power required to pump and also at lower cost. photonic logics will work more efficiently than they do. There will be much less crosstalk, more speed, more gain with simple design.